Q. 14.2( 15 Votes )

How much paper of each shade is needed to make a kite given in Fig. 12.4, in which ABCD is a square with diagonal 44 cm.


Answer :

AC = BD = 44cm

AO = 44/2 = 22cm


BO = 44/2 = 22cm


In ΔAOB,


AB2 = AO2 + BO2


AB2 = 222 + 222


AB2 = 2 × 222


AB = 22√ 2 cm


Area of square = (Side)2 = (22√2)2 = 968 cm2


Area of each triangle (I, II, III, IV) = Area of square /4 = 968 /4 = 242 cm2


Area of lower triangle,


a = 28, b = 28, c = 14


s = (a + b + c)/2


s = (28 + 28 + 14)/2 = 70/2 = 35.


Area(Δ) = √s(s-a)(s-b)(s-c)


Area(Δ) = √35(35-28)(35-28)(35-14)


Area(Δ) = √35×7×7×21


Area(Δ) = 49√15 = 189.77cm2


Area of Red = Area of IV = 242 cm2


Area of Yellow = Area of I + Area of II = 242 + 242 = 484 cm2


Area of Green = Area of III + Area of lower triangle = 242 + 189.77 = 431.77 cm2


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